Inauguration day has fallen on a Sunday six times in the past:
1821, 1847, 1877, 1917, 1957, 1985.
Ronald Reagan’s second swearing-in. From the Senate Inaugurations Committee website: “January 20th fell on Sunday, so Reagan was privately sworn in that day at the White House; public Inauguration on January 21st took place in the Capitol Rotunda, due to freezing weather”